Inverse Laplace Formula

**bkarpuz** · October 12th 2010, 06:24 PM

Dear MHF Residents,

I need the proof of the Laplace inversion formula
$f(t)=\displaystyle\frac{1}{2\pi\mathrm{i}}\display style\int_{\sigma-\mathrm{i}\infty}^{\sigma+\mathrm{i}\infty}F(z)\ma thrm{e}^{tz}\mathrm{d}z,$
where $\sigma$ is a sufficiently large real number, without using the Fourier transform.
Can you please help me in this direction?

bkarpuz

**Ackbeet** · October 23rd 2010, 11:08 AM

Do you have access to Ruel V. Churchill's Operational Mathematics, 2nd Ed.? If so, try pages 176-181. That may be what you're looking for. If you don't have access, let me know.

**bkarpuz** · October 23rd 2010, 11:51 AM

Thanks Ackbeet, it seems that the book is easy of access.

**Ackbeet** · October 23rd 2010, 11:53 AM

Great. Hope that answers your question.

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